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<Title>VertexListGraph</Title>
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<H2><A NAME="concept:VertexListGraph">
VertexListGraph
</H2>

The <I>VertexListGraph</I> concept refines the <a
href="./Graph.html">Graph</a> concept, and adds the requirement for
efficient traversal of all the vertices in the graph.

<H3>Refinement of</H3>

<a href="./Graph.html">Graph</a>

<H3>Associated Types</H3>

<Table border>

<tr>
<td><tt>boost::graph_traits&lt;G&gt;::traversal_category</tt><br><br>
 This tag type must be convertible to <tt>vertex_list_graph_tag</tt>.
</td>
</tr>

<TR>
<TD><tt>boost::graph_traits&lt;G&gt;::vertex_iterator</tt><br><br>
A vertex iterator (obtained via <TT>vertices(g)</TT>) provides access
to all of the vertices in a graph.  A vertex iterator type must meet
the requirements of <a
href="../../utility/MultiPassInputIterator.html">MultiPassInputIterator</a>. The
value type of the vertex iterator must be the vertex descriptor of the
graph.
</TD>
</TR>

<tr>
<td><tt>boost::graph_traits&lt;G&gt;::vertices_size_type</tt><br><br>
The unsigned integer type used to represent the number of vertices
in the graph.
</td>
</tr>

</table>

<h3>Valid Expressions</h3>

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<tr>
<th>Name</th><th>Expression</th><th>Return Type</th><th>Description</th>
</tr>

<tr>
<td>Vertex Set of the Graph</td>
<td><a name="sec:vertices"><TT>vertices(g)</TT></a></TD>
<TD><TT>std::pair&lt;vertex_iterator,&nbsp;vertex_iterator&gt;</TT></TD>
<TD>
Returns an iterator-range providing access to all the vertices in the
graph<TT>g</TT>.
</TD>
</TR>

<tr>
<td>Number of Vertices in the Graph </td>
<td><TT>num_vertices(g)</TT></TD>
<TD><TT>vertices_size_type</TT></TD>
<TD>Returns the number of vertices in the graph <TT>g</TT>.</TD>
</TR>

</TABLE>


<H3>Complexity guarantees</H3>

<P>
The <TT>vertices()</TT> function must return in constant time.

<H3>See Also</H3>

<a href="./graph_concepts.html">Graph concepts</a>


<H3>Design Rationale</H3>

One issue in the design of this concept is whether to include the
refinement from the <a href="./IncidenceGraph.html">IncidenceGraph</a>
and <a href="./AdjacencyGraph.html">AdjacencyGraph</a> concepts.  The
ability to traverse the vertices of a graph is orthogonal to
traversing out-edges, so it would make sense to have a VertexListGraph
concept that only includes vertex traversal. However, such a concept
would no longer really be a graph, but would just be a set, and the
STL already has concepts for dealing with such things. However, there
are many BGL algorithms that need to traverse the vertices and
out-edges of a graph, so for convenience a concept is needed that
groups these requirements together, hence the VertexListGraph concept.


<H3>Concept Checking Class</H3>

<P>
<PRE>
  template &lt;class G&gt;
  struct VertexListGraphConcept
  {
    typedef typename boost::graph_traits&lt;G&gt;::vertex_iterator
      vertex_iterator;
    void constraints() {
      BOOST_CONCEPT_ASSERT(( IncidenceGraphConcept&lt;G&gt; ));
      BOOST_CONCEPT_ASSERT(( AdjacencyGraphConcept&lt;G&gt; ));
      BOOST_CONCEPT_ASSERT(( MultiPassInputIteratorConcept&lt;vertex_iterator&gt; ));

      p = vertices(g);
      V = num_vertices(g);
      v = *p.first;
      const_constraints(g);
    }
    void const_constraints(const G&amp; g) {
      p = vertices(g);
      V = num_vertices(g);
      v = *p.first;
    }
    std::pair&lt;vertex_iterator, vertex_iterator&gt; p;
    typename boost::graph_traits&lt;G&gt;::vertex_descriptor v;
    typename boost::graph_traits&lt;G&gt;::vertices_size_type V;
    G g;
  };
</PRE>

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<HR>
<TABLE>
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<TD nowrap>Copyright &copy; 2000-2001</TD><TD>
<A HREF="http://www.boost.org/people/jeremy_siek.htm">Jeremy Siek</A>, Indiana University (<A HREF="mailto:jsiek@osl.iu.edu">jsiek@osl.iu.edu</A>)
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